An Exact and Fast CBCT Reconstruction via Pseudo-Polar Fourier Transform-Based Discrete Grangeat’s Formula

Low-dose cone-beam computed tomography reconstruction through a fast three-dimensional compressed sensing method based on the three-dimensional pseudo-polar fourier transform

“…As depicted in Figure 2a the 3D conventional FST[ 28 ] shows that (Ŷ φ k , θ j )(ω), the 1D radial FFT of (ɸ φ,θ f )(ρ) along a line with direction of φ k ,θ j , is equivalent to a line of the 3D FFT of f in the same direction, φk,θj ,[ 37 ] where ω is frequency variable.…”

“…(a) Three-dimensional conventional Fourier slice theorem on spherical coordinate, sinogram sampling in the Radon space. (b) Three-dimensional Fourier slice theorem on pseudo-polar grid, linogram sampling in the Radon space[ 28 ]…”

“…Rebinning is transforming the diverging cone beam projections to parallel beam projections. Using the 2D and 3D FST and debt recovery tribunals[ 23 ] in the stage of the rebinning, instead of sinogram sampling in Radon space, an accurate and fast linogram sampling has been proposed by Teyfour et al .,[ 28 ] This algorithm applies 3D PPFT and its inverse on Radon transform (T and ɸ T ) and in pseudo-polar (PP) grid with complexity of O ( N 3 log N ) [ Figure 2b ]. PP grid shown in Figure 2b ] would be of help in bypassing the interpolation stage.…”

“…PPFT has been proven to be a an algebraically precise and fast method in addition to being geometrically faithful and invertible. [ 22 23 24 25 26 27 28 ]…”

“…The main advantage with this article in comparison with the published compressed sensing techniques is the acceleration of the CBCT reconstruction by lowering the CS complexity. To that effect, 3D PPFT-based Radon transform as suggested in[ 28 ] and fast composite splitting algorithm (FCSA) are used for solution. Furthermore, the simultaneous use of Hessian (HS) penalty and 3D wavelet transform in the reconstruction of CBCT images will remove blocky and staircase artifacts while the edges are retained.…”